FIG. 1 shows a well-known field emission electron gun. This gun comprises a cathode 1 made of tungsten or other material, an extraction electrode 2, and an accelerating electrode 3. The extraction electrode 2 produces an electric field that extracts electrons from the cathode 1. The electron beam passing through the extraction electrode 2 is accelerated by the accelerating electrode 3. A voltage of V.sub.1 is applied to the extraction electrode 2 with respect to the cathode 1. A voltage V.sub.0 is applied to the accelerating electrode 3 with respect to the cathode 1. The electrodes 2 and 3 together form an electrostatic lens that acts to focus the electron beam. Therefore, the electron beam passing through the accelerating electrode 3 seems as if it were emitted from a virtual electron source 4 either above or below the cathode 1. Let S.sub.0 be the distance from the extraction electrode 2 to the cathode 1, and let S be the distance from the extraction electrode 2 to the virtual source 4. The distance S varies according to the ratio V.sub.0 /V.sub.1 as shown in FIG. 2. When V.sub.0 /V.sub.1 =1, no lens action occurs between the extraction electrode 2 and the accelerating electrode 3. In this state, the virtual source 4 is located at the front end of the cathode 1, S=S.sub.0, i.e., at the distance S.sub.0 from the extraction electrode 2. As the ratio V.sub.0 /V.sub.1 increases or decreases from unity, the lens action become stronger, moving the virtual source 4 upward away from the tip of the cathode. This region is called the virtual image region.
When the ratio V.sub.0 /V.sub.1 reaches either a threshold value .alpha..sub.1 or another threshold value .alpha..sub.2, the electron beam leaving electrode 3 becomes a parallel beam. The position, or the distance S, of the virtual source 4 then changes from an infinitely remote position above the cathode 1 to an infinitely remote position below it. As the ratio V.sub.0 /V.sub.1 decreases below .alpha..sub.1 or increases above .alpha..sub.2, the position of the virtual source 4 approaches the front end of the cathode 1 from below the accelerating electrode 3. The region less than .alpha..sub.1 and the region in excess of .alpha..sub.2 are known as the real image regions.
Conventional field emission electron guns use electrodes shaped and arranged as shown in FIGS. 3(a)-3(d). The threshold values .alpha..sub.1 of the electron guns equipped with these electrodes range from 0.1 to 0.2, and the threshold values .alpha..sub.2 are in excess of 10.
A scanning electron microscope having a field emission electron gun is required to operate from a low accelerating voltage of about 500 V to a high accelerating voltage of about 50 KV. Normally, the extraction voltage V.sub.1 is changed within a range of about 4 to 8 KV. As the accelerating voltage V.sub.0 is decreased, the ratio V.sub.0 /V.sub.1 decreases below the threshold value .alpha..sub.1. In this case, the electron gun will be operated in one real image region. In the electron gun disclosed in U.S. Pat. No. 3,784,815, the ratio V.sub.0 /V.sub.1 is set less than 1, and a real image is focused by an electrostatic lens without employing other lens action. However, where the accelerating voltage is varied over a wide range, the conditions under which the virtual source is focused onto a specimen by the lens system differ entirely between the case where the virtual source in the virtual image region and the case where the virtual source is placed in one real image region. When the virtual source is shifted into a real image region from the virtual image region, it is difficult to focus the electron beam onto a specimen by the lens system disposed below the electron gun.